The next time a Tour event swings through your town, do yourself a favor and go watch the players practice on a Monday or Tuesday. Be sure to watch their putting routines, how they set up over the ball and most importantly, how they read greens.
You'll notice that, along with their caddies, Tour players critically scan over the green, looking for likely areas where holes will be cut. They inspect the grass and the grain and carefully read any slopes that are apparent to the eye. Once they do that, many players and caddies then take a broader approach and look at not only the green, but also the areas around the green. Often, a mound, collection area, water areas and even bunkers are hints of what direction the green slopes.
For instance, if there's a water feature near a green, it's safe to assume that the green will have some slope toward that water. If there's heavy mounding on one side of the green, it's a pretty safe bet the architect is sloping the green away from those mounds to help the green drain water more effectively. In fact, look for any drains near the green, too. That's a dead giveaway for the low point of the green complex. Bunkers, too, sometimes act as shields from flooding and too much water accumulation on the greens.
Point is, when you're reading greens, don't just read the putting surface. Look at the whole area—the green and all the features around it.